On Semiprime Ample Jordan Rings

Abstract

The purpose of this paper is to point out that the arguments of [2] with slight modification extend the main result of [2] to the case of H satisfying either ACC or DCC on quadratic ideals and they extend [6, Theorem 2] to R being semiprime. Thus we obtainTheorem 1. Let R be a semiprime associative ring with involution ✶ and J a closed ample quadratic Jordan subring of H(R) satisfying either ACC or DCC on quadratic ideals. Then R is Goldie. In this case, J has a Jordan ring of quotients J′ which is a closed ample quadratic Jordan subring of H(R′) where R′ is the associative ring of quotients of R.